Algebra Examples

$16 x^{3} - 144 x^{2} - 81 x + 729$ ; $x - 9$

Step 1

Divide the higher order polynomial by the other polynomial in order to find the remainder.

$\frac{16 x^{3} - 144 x^{2} - 81 x + 729}{x - 9}$

Step 2

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$x$

$9$

$16 x^{3}$

$144 x^{2}$

$81 x$

$729$

Step 3

Divide the highest order term in the dividend $16 x^{3}$ by the highest order term in divisor $x$ .

					$16 x^{2}$
	$x$	-	$9$		$16 x^{3}$	-	$144 x^{2}$	-	$81 x$	+	$729$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $16 x^{3} - 144 x^{2}$

Step 6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 7

Pull the next term from the original dividend down into the current dividend.

Step 8

Divide the highest order term in the dividend $- 81 x$ by the highest order term in divisor $x$ .

Step 9

Multiply the new quotient term by the divisor.

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 81 x + 729$

Step 11

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 12

Since the remander is $0$ , the final answer is the quotient.

$16 x^{2} + 0 x - 81$

Step 13

The remainder is the part of the answer that is left after the division by $x - 9$ is complete.

$0$